Empirical Observations of V BR

2. Chapter 6 pn Junction Diodes: I-V Characteristics Dominant breakdown mechanism is tunneling Empirical Observations of VBR • VBR decreases with increasing N, • VBR decreases with decreasing EG. • VBR : breakdown voltage

3. Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Voltage, VBR • If the reverse bias voltage (–VA) is so large that the peak electric field exceeds a critical value ECR, then the junction will “break down” and large reverse current will flow. • At breakdown, VA=–VBR • Thus, the reverse bias at which breakdown occurs is

4. Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Mechanism: Avalanching High E-field: High energy, enabling impact ionization which causing avalanche, at doping level N < 1018 cm–3 Small E-field: • ECR : critical electric field in the depletion region Low energy, causing lattice vibration and localized heating only

5. Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Mechanism: Zener Process • Zener process is the tunneling mechanism in a reverse-biased diode. • Energy barrier is higher than the kinetic energy of the particle. • The particle energy remains constant during the tunneling process. • Barrier must be thin  dominant breakdown mechanism when both junction sides are heavily doped. • Typically, Zener process dominates when VBR < 4.5V in Si at 300K and N > 1018 cm–3.

6. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region • R–G in the depletion region contributes an additional component of diode current IR–G. • The net generation rate is given by • ET: trap-state energy level

7. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region • Continuing, • For reverse bias, with the carrier concentrations n and p being negligible, • Reverse biases with VA< – few kT/q • Thermal carrier generation in the depletion layer • Carriers swept by electric field and generate additional current

8. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region • Continuing, • For forward bias, the carrier concentrations n and p cannot be neglected, • High carrier concentrations in the depletion layer • Additional carrier recombination in the region that decreases current

9. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region Diffusion, ideal diode

10. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of Series Resistance • The assumption that applied voltage is dropped only across the depletion region is not fully right. Voltage drop, significant for high I

11. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of Series Resistance • As part of the applied voltage is wasted, a larger applied voltage is necessary to achieve the same level of current compared to the ideal. RS can be determined experimentally

12. Chapter 6 pn Junction Diodes: I-V Characteristics Effect of High-Level Injection • As VA increases and about to reach Vbi, the side of the junction which is more lightly doped will eventually reach high-level injection: (for a p+n junction) (for a pn+ junction) • This means that the minority carrier concentration approaches the majority doping concentration. • Then, the majority carrier concentration must increase to maintain the neutrality. • This majority-carrier diffusion current reduces the diode current from the ideal.

13. Chapter 6 pn Junction Diodes: I-V Characteristics High-Level Injection Effect Perturbation of both minority and majority carrier

14. Forward-bias current Chapter 6 pn Junction Diodes: I-V Characteristics Summary Deviations from ideal I-V Reverse-bias current Due to thermal generation in depletion region Due to high-level injection and series resistance in quasineutral regions Due to avalanching and Zener process Due to thermal recombination in depletion region

15. Chapter 6 pn Junction Diodes: I-V Characteristics Minority-Carrier Charge Storage • When VA>0, excess minority carriers are stored in the quasineutral regions of a pn junction.

16. Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach • Consider a forward-biased pn junction. • The total excess hole charge in the n quasineutral region is: • Since the electric field E»0, • Therefore (after all terms multiplied by q), • The minority carrier diffusion equation is (without GL):

17. Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach • Integrating over the n quasineutral region (after all terms multiplied byAdx), QP QP • Furthermore, in a p+n junction, 0 • So: In steady state

18. Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach • In steady state, we can calculate pn junction current in two ways: • From slopes of Δnp(–xp) and Δpn(xn) • From steady-state charges QN and QP stored in each “excess minority charge distribution” • Therefore, • Similarly,

19. Chapter 6 pn Junction Diodes: I-V Characteristics Charge Control Approach • Moreover, in a p+n junction: In steady state

20. Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode • Narrow-base diode: a diode where the width of the quasineutral region on the lightly doped side of the junction is on the order of or less than one diffusion length. n-side contact

21. Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V • We have the following boundary conditions: • Then, the solution is of the form: • Applying the boundary conditions, we have:

22. Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V • Solving for A1 and A2, and substituting back: • Note that • The solution can be written more compactly as

23. Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V • With decrease base width, xc’0: • Δpn is a linear function of x due to negligible thermal R–G in region much shorter than one diffusion length •  JPis constant • This approximation can be derived using Taylor series approximation

24. Narrow-Base Diode I–V Chapter 6 pn Junction Diodes: I-V Characteristics • Because , then • Then, for a p+n junction:

25. Chapter 6 pn Junction Diodes: I-V Characteristics Narrow-Base Diode I–V • If xc’ << LP, • Resulting • Increase of reverse bias means • Increase of reverse current • Increase of depletion width • Decrease of quasineutral region xc’=xc–xn

26. Chapter 6 pn Junction Diodes: I-V Characteristics Wide-Base Diode • Rewriting the general solution for carrier excess, • For the case of wide-base diode (xc’>> LP), Back to ideal diode solution

27. Chapter 6 pn Junction Diodes: I-V Characteristics Wide-Base Diode • Rewriting the general solution for diffusion current, • For the case of wide-base diode (xc’>> LP), Back to ideal diode solution

28. Chapter 6 pn Junction Diodes: I-V Characteristics Homework 5 • 1. (8.14) • The cross-sectional area of a silicon pn junction is 10–3 cm2. The temperature of the diode is 300 K, and the doping concentrations are ND = 1016 cm–3 and NA = 8×1015 cm–3. Assume minority carrier lifetimes of τn0 = 10–6 s and τp0 = 10–7 s. • Calculate the total number of excess electrons in the p region and the total number of excess holes in the n region for (a) VA = 0.3 V, (b) VA = 0.4V, and (c) VA = 0.5 V. • 2. (7.2) • Problem 6.11, Pierret’s “Semiconductor Device Fundamentals”. • Due: 11.06.2012.